How do I move an item on its axis when its rotated?
I think what you're trying to describe is moving along the local axis. Assuming you haven't applied the rotation of the model, you should be able to press g to move the model and then the axis you want to move on TWICE. When you press the axis key twice it goes in that local axis rather than in the world view.
I can go ahead and include some images if you need! Let me know if this helps you out.